Subject: Re: response and question
Date: Fri, 2 May 2003 09:51:09 -0400 (EDT)
From: Tom Goodwillie
To: Don Davis
> The cohomology of any abelian torsion-free group with coefficients
> in any torsion-free commutative ring has no torsion.
Not true. Use Z coefficients. You get an element of order p
in H^2(G) whenever you have an element of H^1(G,Z/p)=Hom(G,Z/p)
that doesn't come from H^1(G)=Hom(G,Z), for example when G is
Z localized at p.